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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
A-76 Mathematical Methods
Set No. 3
1. (a) In matrix notation the system can be written
as AX = B
where
[]
1116
1125
| and
3118
2237
x
AB X y
z
⎡⎤
⎡⎤
⎢⎥
⎢⎥
⎢⎥
==
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
⎣⎦
Applying R
2
R
1
, R
3
− 3R
1
, R
4
− 2R
1
on [A | B]
we have
[]
32
42
1
2
2
1
43
3
1
3
3
11 1 6
021 1
|
02210
041 5
1116
021 1
2
00 3 9
00 1 3
11 1 6
11
01
22
00 1 3
00 0 0
AB
RR
RR
R
RR
R
⎡⎤
⎢⎥
−−
⎢⎥
⎢⎥
−−−
⎢⎥
−−
⎣⎦
⎡⎤
⎢⎥
−−
⎢⎥
⎢⎥
−−
⎢⎥
−−
⎣⎦
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
P(A) = P(A, B) = 3 = no. of unkno
wns. Hence
the system is consistent. It has a unique solu-
tion. By back substitution we hav
e z = 3, y = 2,
x = 1.
(b) In matrix notation line system can be writ-
ten as AX = B where
[]
14714
| 3 8 2 13 and
7 8 26 5
x
AB X y
z
⎡⎤⎡⎤
⎢⎥⎢⎥
=−
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Publisher Resources

ISBN: 9781299446557Publisher Website